Quantum Beating In Photosynthetic Systems using Noisy Light Darin Ulness Department of Chemistry

1. Quantum Beating In Photosynthetic Systems using Noisy Light Darin Ulness Department of Chemistry Concordia College, Moorhead, MN

2. Quantum Beating In Photosynthetic Systems using Noisy Light Darin Ulness Department of Chemistry Concordia College, Moorhead, MN

3. Quantum Beating In Photosynthetic Systems using Noisy Light Darin Ulness Department of Chemistry Concordia College, Moorhead, MN

4. Quantum Biology Magneto-reception Olfactation Enzymes Photosynthesis

7. Fenna-Matthews-Olson (FMO) Complex Green Sulfur Bacteria

8. Fenna-Matthews-Olson (FMO) Complex

9. Energy Transfer Funnel

10. Incoherent Energy Transfer Forster Resonant Energy Transfer

11. Incoherent Energy Transfer Forster Resonant Energy Transfer Another route Coherent Energy Transfer Quantum beating

12. Quantum beating wb P(t) P(t) = ½ + ½cos(wbt) t

13. Quantum beating wb wb P(t) P(t) = ½ + ½cos(wbt) t

14. wb Quantum beating…in a bath L

15. Quantum beating…in a bath wb P(t) L small L L large t

16. Quantum coupling wb wb J

17. J = 0 J = small J = large J = med

18. J = 0 J = large Local Basis Delocalized Basis

19. J = 0 J = large Local Basis Delocalized Basis

20. J = 0 J = large Local Basis Delocalized Basis N N N N

21. J = 0 J = large Local Basis Delocalized Basis N N N N

22. J = 0 J = large Local Basis Exciton Basis

23. J = 0 J = med Local Basis Exciton Basis

24. J Local Basis Exciton Basis Energy t t t t

25. Coherent Light Phase locked

26. Incoherent “noisy” Light Color Locked

27. Time resolution on the order of the correlation time, tc Noisy Light Spectrum Frequency Noisy Light: Definition • Broadband • Phase incoherent • Quasi continuous wave

29. Sunlight is Noisy Light!

30. Material Signal Light field P(t) = P(1) + P(2) + P(3) … P(1) = c(1)E, P(2) = c(2)EE, P(3) = c(3)EEE Nonlinear Spectroscopy P= cE Perturbation series approximation

31. Light source Interferometer A, B, and C beams Local Oscillator (LO) Sample Signal (S beam) Homodyne intensity is observed

32. k A S λ = ±s or ±t φ = z or k s z B C t

33. Noisy Light Spectroscopy Optical coherence theory Perturbation theory: Density operator

34. Difficulty • The cw nature requires all field action permutations. The light is always on. • The proper treatment of the noise cross-correlates chromophores. Solution • Factorized time correlation (FTC) diagram analysis Theoretical Challenges • Complicated Mathematics • Complicated Physical Interpretation

35. Messy integration and algebra Construction Rules Evaluation Rules Set of intensity level terms (pre-evaluated) Set of FTC diagrams Set of evaluated intensity level terms easy Physics hard hard FTC Diagram Analysis

36. Utility of FTC Diagrams • Organize lengthy calculations • Error checking • Identification of important terms • Immediate information of about features of spectrograms • Much physical insight that transcends the choice of mathematical model.

37. Noisy Light Spectroscopy Optical coherence theory Perturbation theory: Density operator Construction of an FTC Diagram k A S s z B C t

38. Noisy Light Spectroscopy Optical coherence theory Perturbation theory: Density operator Construction of an FTC Diagram k A S s z Timeline for signal B C t Timeline for LO

39. Noisy Light Spectroscopy Optical coherence theory Perturbation theory: Density operator Construction of an FTC Diagram k A S s Field Interactions z Timeline for signal B C t Timeline for LO

40. Noisy Light Spectroscopy Optical coherence theory Perturbation theory: Density operator Construction of an FTC Diagram k A S s Material Response z Timeline for signal B C t Timeline for LO

41. Noisy Light Spectroscopy Optical coherence theory Perturbation theory: Density operator Construction of an FTC Diagram k A S Correlated Field Action s z Timeline for signal B C t Timeline for LO

42. Noisy Light Spectroscopy Optical coherence theory Perturbation theory: Density operator Construction of an FTC Diagram k A S s One Example z Timeline for signal A B C B C t Timeline for LO

43. Noisy Light Spectroscopy Optical coherence theory Perturbation theory: Density operator Construction of an FTC Diagram k A S s One Example z Timeline for signal A B C B C t Timeline for LO

44. Noisy Light Spectroscopy Optical coherence theory Perturbation theory: Density operator Construction of an FTC Diagram k A S s One Example z Timeline for signal A B C B C t Timeline for LO

45. FTC diagrams k A S 128 terms = 128 FTC diagrams s z B C t

46. FTC diagrams FTC diagrams k A S 128 terms = 128 FTC diagrams s z Only 3 topological classes! B C t

47. Topological classes of FTC Diagrams • Unrestricted • Singly Restricted • Doubly Restricted

48. Topological classes of FTC Diagrams • Unrestricted • Singly Restricted • Doubly Restricted Strong ! Weak ! Weak !

49. Analytic Results: Unrestricted Strong Signal No quantum beating

50. Analytic Results: Singly restricted Weak Signal Quantum beating